2003MNRAS.341.1020W

We consider the physics of free precession of a rotating neutron star with an oblique magnetic field. We show that if the magnetic stresses are large enough, then there is no possibility of steady rotation, and precession is inevitable. Even if the magnetic stresses are not strong enough to prevent steady rotation, we argue that the local minimum energy state, at fixed magnetic field obliquity, is one in which the star precesses. Since the moment of inertia tensor is inherently triaxial in a magnetic star, the precession is periodic but not sinusoidal in time, in agreement with observations of PSR 1828-11. However, the problem we consider is not just precession of a triaxial body. If magnetic stresses dominate, the amplitude of the precession is not set just by the angle between the rotational angular velocity and any principal axis, which allows it to be small without suppressing oscillations of timing residuals at harmonics of the precession frequency. We argue that magnetic distortions can lead to oscillations of timing residuals of the amplitude, period and relative strength of harmonics observed in PSR 1828-11 if magnetic stresses in its core are about 200 times larger than the classical Maxwell value for its dipole field, and the stellar distortion induced by these enhanced magnetic stresses is about 100-1000 times larger than the deformation of the crust of the neutron star. Magnetic stresses this large can arise if the core is a type II superconductor or from toroidal fields ∼10¹⁴ G if the core is a normal conductor. The observations of PSR 1828-11 appear to require that the magnetic distortion of the neutron star be slightly prolate.